Magnetic Effects Of Current Question 449
Question: The figure shows two infinite semi-cylindrical shells: shell-1 and shell-2. Shell-1 carries current $ i_{1} $ , in inward direction normal to the plane of paper, while shell-2 carries same current $ i_{1} $ , in opposite direction. A long straight conductor lying along the common axis of the shells is carrying current $ i_{2} $ in direction same as that of current in shell-1. Force per unit length on the wire is
Options:
A) 0
B) $ \frac{{\mu_{0}}i_{1}i_{2}}{2\pi r} $
C) $ \frac{2{\mu_{0}}i_{1}i_{2}}{\pi r} $
D) $ \frac{2{\mu_{0}}i_{1}i_{2}}{{{\pi }^{2}}r} $
Show Answer
Answer:
Correct Answer: D
Solution:
Magnetic field at the centre of the shell $ =2\frac{{\mu_{0}}i_{1}}{{{\pi }^{2}}r} $ Force per unit length of the wire $ F=Bi_{2}\times 1 $ $ =[ 2\frac{{\mu_{0}}i_{1}i_{2}}{{{\pi }^{2}}r} ] $
BETA
